- objective
- key activities
- assessment
- What stood out that made it effective?
- What suprised you?
- What went as planned or even better than planned?
- What previous experience prepared you to be effective?
Saturday, July 24, 2010
Reflection: Effective Lesson
Give a very concise summary of an effective lesson you taught:
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I can't praise the iTunes/iPod/iPad problems enough because my class always perks up when I do a problem with this theme. I think the most effective lesson I taught was "Graphing Linear Inequalities" because I explained it with this type of problem. The objective was "TSW graph linear inequalities" and the first key activity was the Do Now in which they were given the problem (iTunes $50 gift card, songs are $1, TV shows are $2, you must spend the whole gift card) and told to graph the linear equation. As they did this they talked about music, TV, and movies that they had recently bought on iTunes. This showed me that they were all definitely engaged. Then I quickly asked a few students to share what songs and TV shows they would buy. We went on to talk about whether you have to spend the entire gift card at once (you don't), and since you don't, how would that change our equation. We then launched into a short talk about inequalities. I gave them the guidelines for graphing linear inequalities (notes), and compared this to graphing inequalities on the number line. We did a few practice problems, and then I had them try some on their own. I assessed by walking around. Finally, we went back to our iTunes problem and converted it to an inequality.
ReplyDeleteThis was effective because I feel that I chunked the lesson well, especially when it came to comparing graphing linear inequalities to graphing linear equations and to graphing inequalities on the number line. Also, the lesson was clearly engaging because of the iTunes aspect. The only thing that surprised me was that it was so engaging! I have a few sleepers in my class, and I didn't have to re-engage/redirect any of them during this lesson because they were all on task. I was glad that they were able to equate the real-world situation into "math language," realizing that not spending the entire gift card meant we needed to set up an inequality. The discussions we had in Methods classes about making the material meaningful for the students really helped me to set up a lesson that ended up being effective, and the possibilities that we brainstormed about were (and will continue to be) invaluable as I continue to plan lessons.
Objective: TSW graph a line given the slope of the line and a point on the line.
ReplyDeleteKey activity: Do Now that focused on a skateboarder at the top of a very steep ramp.
Assessment: Practice problems interspersed throughout the lesson (chunking).
The Do Now could have been much better, as Randy pointed out in my post-evaluation discussion, but overall, the kids were pretty excited about the photo of the skater on top of a ramp, and I noticed a higher level of engagement during the lesson.
My surprise: This wasn't very effective, except as a lesson of what not to do, but one of my best students was completely clueless about the Do Now! It was humbling.
Accidental miracle: Through sketching the skater and ramp scenario, I converted the sketch to a point on a coordinate plane right on the board so the students could directly relate the RL to the mathematical model. It was an "Aha!" moment for both teacher and class, I think.
Previous experience: My C.T. had previously told me that students had a tough time comprehending the concept of slope. As we were going to be covering a lot of ground graphing linear equations and inequalities for the next few weeks, I really wanted to find a way to bring a RL example to the topic in hopes of clearing the slope concept obstacle.
I stumbled upon a great photo of the skateboarder that sparked not only the Do Now, but the approach I took with the lesson.
The objective of the lesson that I taught was a lesson on factoring by finding the Greatest Common Factor. I used an initiation of a video game Nazi Zombies. What I did was to create a scenario where the students had to figure out the ideal formation in rows of five to kill 30 Nazi Zombies and 45 wild dogs. This wasn’t Samurai math, but I won’t wear the headband like Bill. The students at the least seemed amused by the effort. Part of the assignment was to draw the ideal combat formation. Needless to say I saw some interesting pictures. Some were a single shot that hit multiple targets. (This student must be a descendent of someone on the Warren Commission) Some students drew a circle and a person with a gun flipping the bird to the circle. A few I just can’t mention. I think the exercise was effective at bringing out some interest. What surprised me was the student’s didn’t seem to use analytical thinking to approach the problem. I assumed that someone would have gotten the answer by either trial and error or guess and check. This leads me to believe that in the beginning of the school year an effect lesson may be to teach students how to approach a math problem and strategies of finding answers if they don’t know what math to use.
ReplyDeleteI did eventually teach the students how to find the ideal formation by using the Greatest Common Factor. Since the students, at least the males appeared to have a greater interest in that lesson probably because they thought that they could get a higher score in the video game.
The real funny thing about this lesson is that the students kept asking me “How did you know about the video game Nazi Zombies”?
I taught a lesson on ratio and proportion as an introduction to learning about similar triangles. The objectives were: TSW find and simplify a ratio of 2 numbers, and TSW use proportions to solve equations. After I introduced the concept of ratio, I had the kids do an activity that I think they enjoyed. I provided each of them with a tape measure I had made – simply an 11-inch strip of paper with the inches marked. I then told them they were going to measure some of their body parts. After that comment raised some eyebrows and snickers from some of the boys, I bashfully reminded them that we were going to keep things clean in the classroom, and I rephrased my sentence. I had them measure the circumference of the base of their thumb, their wrist, and their ankle. Then they were to compute ratios of thumb-to-wrist, thumb-to-ankle, and wrist-to-ankle. Some of them shared their measurements and a lively discussion of measurement and ratios followed. I gave them a few practice problems and assessed by walking around. I guess what surprised me was how much a simple activity could engage the kids and spark their interest. The previous experience that prepared me to be effective was the first days of student-teaching this summer. I quickly realized that simply lecturing to the kids for 40-50 minutes isn’t an effective way to teach or engage. Providing hands-on activities is key.
ReplyDeleteMy lesson on logs, was effective though it wasn't as entertaining as Tom or Stephen's. I previously had trouble dealing effectively with the wide! range of abilities in my class. I had been catering to the lower end students to the boredom of the more advanced students - and I've been getting away with it since these students are really well behaved. After my last evaluation where Randy stressed "chunking" as a means to spend more time with those who needed more indiv. help, while my "high-flyers" were given a hands-on activity, (and I would talk less) I readjusted this LP to do just that. I feared becoming a "worksheet queen", but I thought of a different way to meet my goals. The goals being that everyone "gets" the topic, while the adv. students aren't waiting for me to finish helping the less adv students. After each new prop of logs, I put several practice problems on the board for the students to try - I walked around to assess. I had several extra problems ready for my high-flyers. Here's what I tried that worked really well: I had this group of advanced students "present" to the other "middle range capabilitiy" students how to approach the more difficult problems (they each did one to share with their classmates). While I worked with the slower students, I had the more advanced students engaged in helping the middle of the road students, and it worked wonderfully. I was previously hung up on having everyone working on the same problem as the same time --- not necessary (duh!) when the goal is to learn the concept/topic, not to complete the exact same problem. I was able to better assess the level of understanding as I wasn't glued to the front of the room, the more advanced students were happy to move around, and the other students were glad to have a peer work with them. My surprise was that several of these advanced students asked me to help explain a topic that they "knew" but had difficulty explaining. In these instances, the level of understanding was reinforced to the advanced students while they were helping to do the same with the middle students.
ReplyDeleteIn the day before, I tried an activity where the students had to make up their own questions to a game (aka Jeopardy style) so they were doing the work, coming up with answers and questions, and having a good time doing it. (I gave each group a topic, and thereby was able to "differentiate" for the levels in my class.) Giving the control of the class to the students was a very positive activity for me and the students, and I think because of this activity the next day's lesson where the students once again took some "teaching power" was successful.
Teaching the slope intercept formula turned out to be an effective lesson for me. The objective was for the students to be able to put an equation in slope/intercept form, analyze what the equation means, and then graph the resulting line by plotting the key elements.
ReplyDeleteI have been admittedly struggling with some of my "warm ups/do nows" but have had more success using real world examples as a transition from the warm up to the body of the lesson. For this lesson I used information I learned about Subway's $5 foot long marketing campaign to lead into a lesson on how a linear equation equates to the demand curve for a product. The transition naturally leads into a later lesson on solving linear systems. The students enjoyed the discussion on how Subway came up with the idea and based on their answers to my questions, understood the material. They were providing most of the information I had planned to teach (which was an unexpected bonus) so I adapted by guiding their discussions and filling in a few missing pieces. As mentioned by others in their posts, using topics the students find interesting is half the battle in keeping them engaged.
The micro-teaches were definitely a good learning tool and helped me understand where problems were likely to occur. I have yet to put together what I consider a complete lesson and sense my approach is getting a bit stale. Next week I hope to change the routine a little to keep the students on their feet and to prevent them from reverting back to the problems we had the very first week.
I taught an effective lesson on integers. The objective was TSW multiply and divided positive and negative integers. It was the activity that I did that was most effective. I had the students make signs with a + on one side and a - on the other. I wrote problems on the board and they held up their signs to show whether the answer was positive or negative. The students really got into it and it was fun. It was an assessment too, because I could see who was getting the right answers and who wasn't. I did this the day after our core session on engaging the reluctant learner where we did something similar.
ReplyDeleteMy most effective lesson to date was one on probability. (That said, I still look back and think of what I could have done differently to make it better!) It was effective because it completely engaged the students and seemed to hit on an area of interest for each one of them. Our objectives were to find probabilities during our activities, compare experimental and theoretical probability, and (based on that data) use probabilities to make predictions about uncertain occurrences.
ReplyDeleteThe key activity was the creation of a grid showing the theoretical outcomes for tossing a pair of dice. After listing the likelihood of each outcome _ and discussing the meaning and what they could expect to see- the students used dice to do their own experiment, and recorded their results. This went remarkably well, as I worried I could have dice flying through the air and across the floor. Not the case! Each student actually completed the exercise and filled out the information (definitely a first for 100 % participation). There is no doubt these hands-on activities are what the students want and what will keep them engaged...I try to incorporate some sort of tangible exercise in every lesson.
As assessment, other than walking around to be sure everyone was following through with the exercise, I gave a short pop quiz (though I do NOT call it that to them) asking some questons about the exercise they completed...for example, in their own words, the difference between experimental and theoretical probability. It was a fun day for both teacher and students!
I had taught a lesson, but we had not completed it in the 50 minute period. I also found through the practice problems that I had given the class that they did not fully grasp the concept. I spoke to my consulting teacher and we agreed that I would continue with the lesson, and give them more practice with a class worksheet.
ReplyDeleteWe had completed the instructional part of the lesson and were ready to go onto the work sheet. I was toying with the idea of doing something different, because we had discussed “Samurai Math” in class. So I said to the students that we could either do a worksheet like we had done in the past, or we could do a “Math-Relay.” They asked what that was. I asked if anyone had seen a relay race on a track. Some said they had. I explained that we would divide the class into three relay teams. The dry-erase marker was the baton. The problems we were doing had four steps. The first person on the team would do the first step. He or she would then pass the “baton” to a team member, who would do the next step until the problem was solved. The team who finished first would get a point. No one could go to the board a second time until all the team members had been to the board first. You had to sit down before the next member of the team could go to the board, so there would be only one member from a team up at a time. The team members could help their teammate at the board by giving them the answers. One student asked what was in it for the class if they did this “Math Relay.” I said that the winning team would get a double set of tickets for the raffle. I let the class form their own teams. I had to ask a student to join a team that was one person short.. One student volunteered to join the team that was short, even though she would have preferred to be with her friends.
I wrote a simple problem on the board and gave the green baton to the green team and the blue baton to the blue team. The remaining team did not like my color baton so one student had her own dry-erase marker, and they became the purple team. The teams started the problem, and one student combined two steps. The other teams’ members start shouting that he was cheating. His team members said he was not. The teams finished the problems, and I had to make a ruling about whether the team cheated, because they had come in first. I ruled that since I had not made it clear how the steps were to be done, it was not cheating in this case, but then I clarified the rules for the next round. The students were excited and shouting out to their team members how to do the problem. We made quite a ruckus that disturbed the other class in our room. We did not cover as many problems as I would have liked, but the students were much more engaged than they ever would have been if we done the worksheet at the students’ desks.
I was surprised at the amount of engagement we had, because the previous day’s session had not gone as well as I would have liked. Everyone participated. Students who I had problems getting to go to the board were willing to do so. The best assessment of the project was that students who did not usually participate were as involved as students who always participated.
Objective: TLW solve and graph compound linear inequalities.
ReplyDeleteKey Activities: Venn Diagram & Poster Making
Assessments: Students worked problems and presented to the class, then displayed their problem.
This has been my favorite lesson to date. The Do Now that I passed out had the students solve some basic inequalities and list facts about football and basketball. We started the class completing a large Venn diagram comparing and contrasting the two sports. This led right in to the topic of compound inequalities.
One of my greatest AHA's was noticing that the "ands" were in the middle with the "ors" on the outside. When I started out with the Venn Diagram that aspect had not occured to me, but it was a great visual of what an "and" or "or" graph looks like.
One of my assessments/activities paired the students in small groups. Each was given an envelope with pieces of a compound inequality in it. They had to put the pieces in order and tape them to a poster piece. Finally they presented to the class their poster and explained the inequality. This used markers and tape and really got everyone involved.
I think my previous observation helped prepare me for this. One of my biggest areas to work on was debriefing my students after we did an activity to make certain they understood how the activity tied in to the subject matter. I felt the explanation of the Venn Diagram really brought the concept home.
No, really. How did you know about the video game Nazi Zombies? :^) OK, back on topic.
ReplyDeleteMy objective for the day was “Solve multistep equations.” The class began with a summative assessment (a 20-minute quiz) on the prior section.
My initiator following the quiz was to select a car from a used-car pamphlet, record the total cost, estimate (guess) the monthly payment if you pay for it in 3 years (36 payments), write a word equation to determine the total cost, and write the equation corresponding to the word equation. This was an example of an equation of the earlier topic (Solve an equations using multiplication and division).
After discussing the initiator, I told the students that the dealer insists on a down payment to drive the car off the lot. The students revised their word equations and math equations, gaining the insight that their monthly payment would be less due to the up-front payment. This is an example of solving a multistep equation.
The students then practiced solving multistep equations (writing at their desks and sharing solutions on the board). I then gave a pop quiz on solving multistep equations.
What surprised me was that I seemed to need just as much energy to engage them in this activity as in other activities that were more cut-and-dried. It was a different need for engagement – they wanted to just read the brochure. I had to go group-by-group to force them to pick in order to be able to take away the brochure.
The use of the real-life example provided some important information to students about buying a car – not all students were familiar with the idea of a down payment, nor that the down payment would be reflected in lower monthly payments. Connecting math to life skills is important to help them understand the relevance of algebra in real life, and helps to engage them in learning math.
I think the lesson went about as well as I had planned, but I think I can use it more effectively the next time by scaffolding the activity better on the Do Now, and by more smoothly engaging the students in the work and taking away the brochures sooner.
Although they struggled at first with the Scientific Notation lesson (some of their prior knowledge was weak, i.g., decimals and fractions!), after a high-level DoNow (calculating the number of miles Captain Kirk would go to reach Vulcan 90 light years away), they were very engaged with the material.
ReplyDeleteAs with my colleague's students, there is a wide range of ability in the class, and the more advanced students get bored while I have to explain a simple example for the slower students. I have to say, although I have yet to successfully tackle this, reading the other posts here is a godsend, because everyone has good experiences to share, so we can benefit from one another.
For my lesson:
OBJECTIVES - Evaluate & multiply by powers of 10; Convert between Standard & Scientific Notation
KEY ACTIVITIES - the DoNow Scientific Notation - Kirk-to-Vulcan worksheet; Practice problems, Assignment
ASSESSMENT - Walk-around (ad hoc); Assignment Correction
What stood out that made it effective?
The 'calculate light speed' problem from the DoNow
What suprised you?
Too many students had poor prior knowledge, and I wondered how that happens (getting to grade 8/9, and not being solid with decimals and fraction!)
What went as planned or even better than planned?
The DoNow
What went worse than planned?
The lecture got bogged down in a few example problems because of the poor prior knowledge with some of the students
What previous experience prepared you to be effective?
The culmination of Core, Method, and Student Teaching, and especially reading my colleagues blog posts and ad hoc discussions in- and outside class with them. In many cases, there is nothing better than sharing knowledge one-on-one
There was one "Do Now" that my class did that was so cool to watch! I'll talk about this one quickly, then get to another lesson:
ReplyDeleteTHINK, PAIR, SHARE:
We were introducing the coordinate plane.
• objective
Objective for this portion of class was TSW plot points in a coordinate plane/ TSW label plotted points in a coordinate plane.)
I wanted to do a discovery lesson for the "Do Now," so I told them the legend (apocryphal, I'm sure) of Descartes's epiphany while lying sick in his bed: He was gazing up at the ceiling, watching a fly move from one spot to another, and he pondered how to describe the exact location of the fly at any given moment (and BOOM! -- analytic geometry was born... I know, fairy tale, I'm sure, but it grabs the attention.)
I did not tell them what Descartes's conclusion was.
• key activities
I gave them a picture of a blank rectangle ceiling with a picture of four labeled flies. Since they were supposed to be too sick to move, their task was to phone the upstairs neighbor (who had an identical floor plan). Since there is no other way to kill a fly, the task was to tell the neighbor exactly where each fly was. The upstairs neighbor would subsequently drill a hole in the appropriate spot, thereby terminating the little nuisances' existence. They were given rulers.
The students were then to share with their designated partner the system they'd created, and each partner's job was to see if they could find any holes in their partner's system (lack of specificity, etc). Then each pair was to share the results with the class.
• What suprised you?
The results were AWESOME! One pair created a "chessboard" system that mimicked the game of battleship. There was a letter "axis" (they didn't use this word, of course) and a number axis, so a fly could be in the "C-3" box. Then, for better accuracy, they described the fly's position in the box ("upper right-hand corner").
Another pair essentially
created a variation of the polar coordinate system. The "origin" was in the center of the box, and each point was determined by the vertical distance from O and the angle from the "y axis" (again, didn't use math words).
ReplyDeleteWe then discussed Descartes's solution.
If I were to do this again, I would have them act out the phone call with a partner: Each would be given a blank rectangle, and they would guess and mark the positions of the flies based solely on the phone conversation with their partners.
• What stood out that made it effective?
I think it was the "create" element that got them engaged. I wasn't sure this would take off, but they really got into it.
• What previous experience prepared you to be effective?
1. Bloom's discussion, 2. Learning to use "Do Now" as a launch pad for the new content.
• assessment
The assessment came late as a "pop quiz"r, after we had practice plotting and labeling points.
I was actually planning on talking about a different lesson -- one on formulas and functions -- but I wound up writing so much on the one above, I don't want to bore you guys. Here's are a two quick things that worked well on the formulas/functions lesson:
1. RRLE that they really got into:
Storm problem. We've all learned at some point about finding the distance of a storm by counting seconds btn lightning and thunder. I stole a problem in a math book that used this formula. Amazingly, none of them had learned this yet, and they were fascinated! We got into a discussion about the speeds of light and sound. It was the week after July 4, and we talked about seeing vs. hearing fireworks. I asked them if they thought the same formula would apply. I relayed Dr. Fritz's story about hearing a start gun twice at a race -- one through walkie talkie (radio waves), one through the air (speed of sound). They asked about what's going on when you're talking to someone on the phone, both parties with the radio on, and you hear a delay of the radio station.
This admittedly strayed a little from the objective, but I felt OK about it because they were so interested, and it made a connection to their experience (and maybe their past/future science class).
2. SImple but ENORMOUSLY effective tip I got from my CT: Always work left-to-right on the board. Yeah, it seems so obvious I shouldn't have to mention it, but this tip made a night-and-day difference in my lessons. It organized the sequence and logic of what we're discussing in a visual way.
For me, some of the most effective lessons have taken advantage of this tip by starting simple on the left (or by starting with a RRLE on left), then making one slight change, or adding one bite of complexity to the immediate right, and so on. Then, as the lesson progresses, if I can relate each new step to the examples on the left -- often going all the way back to the beginning -- I've found that the material really sinks in more effectively. Again, my apologies if this was obvious for everyone else, but Friday's lesson went really well, and I think it stemmed from the RRLE and this technique.
Did I say "quick"?
ReplyDeleteEvan:
ReplyDeleteI, too, had to be reminded to write left-to-right on the board. I didn't realize I was all over the place.
Don't worry about quick when your topic is so interesting, Evan! Love it!!!
ReplyDeleteObjective: TSW solve and graph linear inequalities
ReplyDeleteKey activities: “Do Now”
Assessment: walking around and questioning students
Like Steven said I have also realized what I needed to do differently to make the lesson more successful. I gave this problem to the students as an activity but Randy pointed out that this should be the “Do Now” So here it is, Coby needs to make $ 600 or more to go to a summer basketball camp. He has decided to provide 2 types of services; walking a dog for $ 10 and mowing lawn for $20.
1.)Write an inequality that represents Coby’s income from dog-walking and lawn mowing? Graph this inequality. Please provide 3 set of possible solutions.
I have broken it down further by asking:
a. How much money can Coby earn by walking dogs?
b. How much can he earn by mowing lawns?
c. How much can he earn all together if he wants to make $600 or more?
2.)This second part would have been the intro to systems of inequalities but I recognized that I cannot jam the two objectives into one lesson.
It said: Beside all the information above, Coby knows that he can walk more than 5 dogs because his neighbor Mrs. Jones has 5 dogs. Graph the inequalities (from part 1. and 2.) and shade the intersections? By marking these points on the coordinate plane, I would ask is A, B or C a solution, explain why or why not?
I believe it was effective because students could easily relate to a dilemma like this problem.
It surprised me that all students paid attention to this example and they were interested in how much could Coby make. I was also a bit surprised that my original “Do Now” that included parts of how to solve inequalities turned out to be too hard for the students to figure out although to me it seemed simple.
By now, I understand that you should know your audience very well in order to present them with challenging problems that are at the appropriate level for the class.
To be effective, Randy’s words were ringing in my ears that students would be able to better grasp mathematical concepts if they are presented with relevant real life problems. Therefore I tailor my lesson plan to include a RRLE as much as I can depending on the material.
Melinda,
ReplyDeleteI like your RRLE. I'm not surprised they were into this one. Who doesn't want to know how to maximize their income? Permission to steal...?
Effective lesson plans require: Good objectives; Tie in to prior knowledge; Frequent effective assessments; Good transitions; and student engagement.
ReplyDeleteI did a recent one on the properties of triangle inequalities I used a discovery where the students had to make triangles out of different size straw color coded straw segments. I had them try to understand what is required of the segments lengths in order to make a triangle. I got them engaged by putting them in groups and setting up competitions. sweat reward seem to work well. You also need to have them do things fairly often to keep their attention and them learning. The problem for me here was that they seemed to get the material too quickly and I needed more backup material to make up for this. This class has become so engaged as of late that they go through material much faster than they did only a few days back.
I have to go with Tom's opinion concerning iTunes. I did a lesson on multiplying polynomials which included a real world analysis of single track downloads (by year), and average price per download (by year). From this, a polynomial for calculating the total revenue of downloads for a particular year. I obtained the data from the International Federation of the Phonographic Industry (http://www.ifpi.org/).
ReplyDeleteThe objective was to multiply polynomials and apply this to a real life situation. I took the students througha couple of problems just to get in some practice. I then showed them a polynomial which calculated the number of downloads for a particular year, and a binomial indicating the average price for a download for a particular year. The student multiplied the downloads polynomial with the price-per-download binomial to come up with a polynomial for calculating total revenue from downloads. My usual walkabout-the-class was my assessment.
The numbers in this application were pretty ridiculous:
Downloads:
D = 92x^3 - 1832x^2 + 12160x - 26120
Price per download:
P = .002x + 0.98
Total revenue:
0.184x^4 + 86.496x^3 - 1771.64x^2 + 11864.56x - 25597.6
(for years 2005 and after)
Of course, I had the students use their calculators to come up with the revenue formula. I was really amazed on how well they stuck with it. There was absolutely no comments about the exercise being unreasonable (and I did mentioned thay they were free to make that complaint). I was also amazed the percentage of students that had the answer correct, which tells me there was a greater degree of determination to get this problem correct. I did mention that although I would never give this type of a problem on a test, this was an example of the number crunching done in the real world.
The exercise obviously reinforced the concept of multiplying polynomials. In the words of Stephen, this whole exercise was an accidental miracle.
BTW - I'm stealing everyone else's lesson >:)